Consider the quadratic equation with real coefficients and

MATHEMATICS · Subjective · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

Consider the quadratic equation

ax^{2}+bx+c=0

with real coefficients

a\,(\neq 0),\,b

and

c

. Answer the following: (i) Write the condition on

a,\,b,\,c

that guarantees the equation has two equal real roots. (ii) Using the result of (i), justify algebraically that the graph of

y=ax^{2}+bx+c

touches the

x

-axis at exactly one point and find the

x

-coordinate of this point in terms of

a

and

b

. (iii) The quadratic

3x^{2}+kx+4=0

is required to have its double root less than

-2

. Show that no real value of

k

satisfies this requirement.